Number 4 cylinder is cold as ice

Prior to my annual I was experiencing backfiring whenever at low rpms. Either on startup or whenever pulling the power to enter the pattern. On start up it would clear pretty quickly. In the air everything was fine. Enter the pattern and pull power and you got the unwanted few pops. On day my A&P pulled the cowl and found number 4 to be cold shortly after startup. We changed plugs and all was well. It started up again so at my yearly check up we chose to replace the rear mag plate with new plug wires included. All plugs were cleaned and recapped. The next 4 flights were uneventful. After my last 20 min flight the plane sat for a few hours and on restart the is toms returned. After several attempts over several days number 4 is as cold as ice. The engine runs very rough and will not run over 1700-1800 rpms. On hand turning the prop compressions seem to be normal on all cylinders. Any thoughts? Stuck valve(s) perhaps?

compression check

Do a compression check if you have good compression it's not a stuck valve. But if you just did a condition inspection I'm sure you did that. Maybe a plugged injector if it is injected. Maybe a bad coil if it is electronic ignition.

Ran compression checks during condition inspection. All were in the green. I am running a carb setup. And wouldn't a bad coil affect all cylinders?

fouled plugs? do you lean on the ground?
Sound exactly as my old C-152. the 0-235 was know to have a plug fouling problem and could foul a plug very quickly if not leaned aggressively on the ground.
The fact that you changed plugs and the problem went away also points in that direction. On the other hand, I think if your A&P replaced the plugs, they would have told you if the plugs were caked in lead or not. (one bad plug on one cylinder will cause the cylinder to be cold)

Do you have a primer line on #4? If so check that it's not cracked and leaking extra air into the cylinder. If no primer check that there is a plug in place in the cylinder.

The cylinder has plugs top and bottom and as noted flew well the same day. I make a habit of leaning both on the ground and at cruise altitude. I am guessing a stuck valve is going to be the culprit in this case with the reading I've done over the past few days.